# The following data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetime of the components

## Solution :

The following (60 – 80) has the maximum frequency. Therefore, this is the modal class.

Here, l = 60, h = 20, $$f_1$$ = 61, $$f_0$$ = 52 and $$f_2$$ = 38

Now, let us substitute these value in the formula

Mode = l + ($$f_1 – f_0\over 2f_1 – f_0 – f_2$$)$$\times$$h

= 60 + ($$61 – 52\over 122 – 52 – 38$$)$$\times$$ 20

= 60 + $$9\over 32$$ $$\times$$ 20

= 60 + 5.625 = 65.625

Thus, the modal lifetimes of the components is 65.625 hours.